Non-dimensionalization of Helmholtz equation and the nature of the Alfvenic turbulence

I redefined Reynold number in a different situation, the Helmholtz equation which represents the time-independent wave equation, $\nabla^2 A+k^2 A=0$ Now i consider wave number as Reynold number per linear dimension, $L^2\nabla^2 A+R_e^2 A=0$ the important non-dimensional parameters for MHD are Reynold, Magnetic Reynold and Prandtl numbers, $R_e.P_m=R_{em}$ then we find, $P_m^2L^2\nabla^2 A+R_{e_m}^2 A=0$ where the $\nabla^2$ is laplacian and $A$ is the Amplitude.